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This course introduces the operational and denotational semantics of PCF and examines the relationship between the two. Topics: Syntax and operational semantics of PCF, Activity Lemma, undefinability of parallel or; Context Lemma (first principles proof) and proof by logical relations Denotational semantics of PCF induced by an interpretation; (standard) Scott model, adequacy, weak adequacy and its proof (by a computability predicate) Domain Theory up to SFP and Scott domains; non full abstraction of the standard model, definability of compact elements and full abstraction for PCFP (PCF + parallel or), properties of order-extensional (continuous) models of PCF, Milner's model and Mulmuley's construction (excluding proofs) Additional topics (time permitting): results on pure simply-typed lambda calculus, Friedman 's Completeness Theorem, minimal model, logical relations and definability, undecidability of lambda definability (excluding proof), dI-domains and stable functions Homepa...

ion for PCF Preliminary Announcement Martin Hyland and Luke Ong 26th July 1993 This note is (intended to be) released in conjunction with a preliminary announcement of Abramsky, Jagadeesan and Malacaria entitled Games and Full Abstraction of PCF. Like Abramsky et al. (but independently), we have found an intensionally fully abstract model for pcf [Plo77]. Our model is a Cartesian closed category of Scott domains all of whose compact elements are definable in pcf. Using Stoughton's Theorem [Sto88], the model can be extensionally collapsed by means of a continuous homomorphism to the least fixpoint, order-extensional, fully abstract model which is shown to be unique by Milner [Mil77]. It is unclear at this stage how our model relates to that of Abramsky et al. Our model of computation is based on a kind of game in which each play consists of a dialogue of questions and answers between two players. This approach is very concrete and in nature goes back to Kleene [Kle78] and Gandy in o...

The class of monotone input/output automata has been shown in the authors' previous work to be a useful operational model for dataflow-style networks of communicating processes. An interesting class of problems arising from this model are those that concern the relationship between the input/output behavior of automata to the structure of their transition graphs. In this paper, we restrict our attention to the subclass of determinate automata, which compute continuous functions, and we characterize classes of determinate automata that compute: (1) the class of functions that are stable in the sense of Berry, and (2) the class of functions that are sequential in the sense of Kahn and Plotkin. 1 Introduction The results reported in this paper are part of a general program aimed at relating the input/output behavior of dataflow-like networks of communicating processes, modeled as automata, to the structure of their transition graphs. In previous work [12], we identified the class of mono...